On the proof of continued fraction expansions for irrationals (Q1070261)
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scientific article; zbMATH DE number 3935115
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the proof of continued fraction expansions for irrationals |
scientific article; zbMATH DE number 3935115 |
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On the proof of continued fraction expansions for irrationals (English)
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1986
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\textit{J. Shallit} [ibid. 11, 209-217 (1979; Zbl 0404.10003); and 14, 228- 231 (1982; Zbl 0481.10005)] gave an explicit description of the simple continued fraction expansions for the numbers \(\sum^{\infty}_{k=0}u^{-c(k)}\) where \(u\geq 2\) is an integer and c(k) is any sequence of positive integers which grows sufficiently quickly. The author presents a version of the proof which is based upon a matrix notation for the convergents of continued fraction.
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irrationals
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simple continued fraction expansions
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matrix notation
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convergents of continued fraction
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